Before taking the square root, combine the numbers inside it. What is $13+12$?

Once you have a number inside the square root, think: what nonnegative number multiplied by itself equals that number?

In Desmos, type sqrt(13+12) into an expression line. Look at the numerical output that Desmos gives for this expression; that value is $f(13)$.

The function is defined as $f(x)=\sqrt{x+12}$. This means that for any input value of $x$, you first add $12$ to $x$ and then take the square root of the result.

To find $f(13)$, replace $x$ with $13$ in the expression for $f(x)$:

Add the numbers inside the square root:

So now we have:

The square root of $25$ is $5$ because $5\times 5=25$. Therefore,

So the correct answer choice is B) 5.